% Taken from macros22, 28/01/2007

% This is a LaTeX version of Pformula, where \a, \sp, \S, \H, \t have been changed or deleted because they needed \renewcommand.

% This package requires other packages among \usepackage{amssymb,amsfonts,amsmath,amscd,latexsym}  

\NeedsTeXFormat{LaTeX2e}[1999/12/01]
\ProvidesPackage{Pformel}

\newcommand \bsm {\left(\begin{smallmatrix}}
\newcommand \esm {\end{smallmatrix}\right)}
\newcommand \bla {\left\{\begin{array}{l} }
\newcommand \ela {\end{array}\right. }

\newcommand \bea {\begin{eqnarray}}
\newcommand \eea {\end{eqnarray}}
\newcommand \bee {\begin{eqnarray*}}
\newcommand \eee {\end{eqnarray*}}
\newcommand \nn  {\nonumber}
\newcommand \sst {\scriptscriptstyle}

% Instead of \sp: 'space comma space'
\newcommand \scs   { \ \ \ , \ \ \ }

\newcommand \tsum  { {\textstyle \sum} }

% Instead of \deg
\newcommand \degf {{-\frac{1}{2b}}}
\newcommand \tdeg {{\tfrac{1}{2b}}}

\newcommand \p {\partial}
\newcommand \pp[1] {{\frac{\p}{\p #1}}}
\newcommand \ppd[1] {{\frac{\p^2}{\p #1 ^2}} }
\newcommand \ppt[1] {{\frac{\p^3}{\p #1 ^3}} }
\newcommand \ppl[1] {{\frac{\delta}{\delta #1}}}

\newcommand \om {\omega}
\newcommand \g {\gamma}
\newcommand \vf {\varphi}
\newcommand \s {\sigma}
\newcommand \G {\Gamma}  
\newcommand \e {\epsilon}
% Instead of \a
\newcommand \al {\alpha}
\newcommand \be {\beta}
\providecommand \up {\Upsilon_b}  % works only if command does not already exist 
\newcommand \vt {\vartheta_1}

\newcommand \rar {\rightarrow}
\newcommand \lrar {\leftrightarrow}

\newcommand \bg {\bar{\gamma}}

%\alp was formerly \ap which apparently already existed
\newcommand \alp {\alpha'}
\newcommand \bal {\bar{alpha}}
\newcommand \bz {\bar{z}}
\newcommand \bw {\bar{w}}
\newcommand \bx {\bar{x}}
\newcommand \bp {\bar{\partial}}
\newcommand \bq {\bar{q}}
\newcommand \bL {\bar{L}}
\newcommand \bJ {\bar{J}}
\newcommand \tJ {\tilde{J}}
\newcommand \tq {\tilde{q}}
\newcommand \tth {\tilde{\theta}}
\newcommand \ttau {\tilde{\tau}}

\newcommand \Tr {{\rm Tr }\ }
\newcommand \id {{\rm id } }
\newcommand \sgn{ {\rm sgn} }
\newcommand \sign{ {\rm sign} } 
\newcommand \cst {{\rm constant}}
\newcommand \Res {{\rm Res }}

\newcommand \Z {\mathbb{Z}}
\newcommand \N {\mathbb{N}}
\providecommand \R {\mathbb{R}}
\newcommand \C {\mathbb{C}}
\newcommand \Q {\mathbb{Q}}
% Instead of \S
\newcommand \Sp {\mathbb{S}}

\newcommand \la {\left\langle}
\newcommand \ra {\right\rangle}
\newcommand \lla {\langle\langle}
\newcommand \rra {\rangle\rangle}

\newcommand \uq  {U_q(sl_2)}
\newcommand \asl {\widehat{s\ell_2}}
\newcommand \aslt {\widehat{s\ell_3}}
\newcommand \SLC    {SL(2,\C)}
\newcommand \SLR    {SL(2,\mathbb{R})}
\newcommand \SLU    {SL(2,\mathbb{R})/U(1)}
\newcommand \USLR   {\widetilde{SL}(2,\mathbb{R})}
% Instead of \H
\newcommand \Hp      {H_3^+}

\newcommand \gsin[2] {\left[\!\! \begin{array}{c} #1 \\ #2 \end{array}\!\! \right]}

\newcommand \six[6]{
 _{#1\, #2}\left[\!\begin{array}{cc}
#5 & #4 \\ 
#6 & #3
\end{array}\!\right]}

% written for Clebsches
\newcommand \dft[6]{ \left(\begin{array}{ccc} #1 & #2 & #3 \\ #4 & #5
    & #6 \end{array} \right) }
    
\newcommand \tft[6]{ \ _3F_2\!\!\left.\left(\!\!\begin{array}{c} #1\ \ \ #2\ \ \ #3 \\ #4\ \ \ \ #5 \end{array}\!\right|#6\!\right)}

\newcommand \tgt[5]{ G\!\left(\!\!\begin{array}{c} #1\ \ #2\ \ #3 \\ #4\ \ #5 \end{array}\!\!\right)}

\newcommand \Fsep { \ , \ }

\newcommand\vect[2]{ \left( \hspace{-2mm}\begin{array}{c} #1 \\ #2  \end{array}\hspace{-2mm} \right)}
\newcommand\trip[3]{ \left( \hspace{-2mm}\begin{array}{c} #1 \\ #2 \\ #3 \end{array}\hspace{-2mm} \right)}